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Simplifying 8x2 + -47x + -75 = 0 Reorder the terms: -75 + -47x + 8x2 = 0 Solving -75 + -47x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.375 + -5.875x + x2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + -5.875x + 9.375 + x2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + -5.875x + x2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + -5.875x + x2 = 0 + 9.375 -5.875x + x2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 -5.875x + x2 = 9.375 The x term is -5.875x. Take half its coefficient (-2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. -5.875x + 8.62890625 + x2 = 9.375 + 8.62890625 Reorder the terms: 8.62890625 + -5.875x + x2 = 9.375 + 8.62890625 Combine like terms: 9.375 + 8.62890625 = 18.00390625 8.62890625 + -5.875x + x2 = 18.00390625 Factor a perfect square on the left side: (x + -2.9375)(x + -2.9375) = 18.00390625 Calculate the square root of the right side: 4.243101018 Break this problem into two subproblems by setting (x + -2.9375) equal to 4.243101018 and -4.243101018.Subproblem 1
x + -2.9375 = 4.243101018 Simplifying x + -2.9375 = 4.243101018 Reorder the terms: -2.9375 + x = 4.243101018 Solving -2.9375 + x = 4.243101018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = 4.243101018 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = 4.243101018 + 2.9375 x = 4.243101018 + 2.9375 Combine like terms: 4.243101018 + 2.9375 = 7.180601018 x = 7.180601018 Simplifying x = 7.180601018Subproblem 2
x + -2.9375 = -4.243101018 Simplifying x + -2.9375 = -4.243101018 Reorder the terms: -2.9375 + x = -4.243101018 Solving -2.9375 + x = -4.243101018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = -4.243101018 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = -4.243101018 + 2.9375 x = -4.243101018 + 2.9375 Combine like terms: -4.243101018 + 2.9375 = -1.305601018 x = -1.305601018 Simplifying x = -1.305601018Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.180601018, -1.305601018}
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